1. Field of the Invention
The present invention relates to golf clubs, and specifically to an improved method of dynamically matching a set of clubs.
2. Prior Art
Attempts to "match" a set of golf clubs are well known in the prior art. Basically, the art of matching golf clubs may be summarized in four categories:
1. Swing-weight matching. This method of matching, detailed in U.S. Pat. Nos. 1,594,801 and 1,953,916, is a static measurement technique to match a set of clubs. The "swing-weight" of a given club is determined by placing the club across a knife-edge or fulcrum located at an arbitrary fixed distance (usually 12 to 14 inches) from the grip end of the shaft and placing sufficient weight at the very tip of the grip end of the shaft to balance the club. This weight is then termed the "swing-weight". The swing-weight method of matching clubs assures a gradual variation of the dynamic parameters, the mass, the first moment, and the second moment (monent of inertia) of the clubs over the set of clubs. Most golf clubs now available to golfers are swing-weight matched.
2. First moment matching. U.S. Pat. No. 4,058,312 describes this method of matching a set of golf clubs and is based on the assumption that it is the first moment that determines the feel in the swing of a golf club and, therefore, a set of clubs with identical first moments will provide the golfer with better control. This patent describes a set of clubs matched according to their first moment about a wristcock axis at some standard distance from the grip end of the club.
3. Moment of inertia matching. Various methods for matching a set of clubs according to their moments of inertia are described in U.S. Pat. Nos. 3,703,824, 3,698,239, and 3,473,370. In essence, each of these methods strives to achieve the same moment of inertia about some wristcock axis for each club of a set. This moment of inertia method of matching is based on the assumption that it is the second moment (the moment of inertia) that determines the feel and the swing of a golf club and, therefore, clubs with identical second moments will provide the golfer with better control.
4. Mass, first moment, and second moment matching. A set of golf clubs are matched when the three dynamic parameters, the mass, first moment about some wristcock axis, and second moment about the same wristcock axis, are respectively the same for all clubs of the set. The first moment and second moment parameters are dependent on the distribution of mass in the club. One method of finding a distribution of mass for each club that will satisfy this criteria of matching is described in U.S. Pat. No. 4,128,242. This patent discloses a method for matching golf clubs in which a single mass slug is placed at some point, different for each club, along the shaft of each club. This method, while it does work to produce matched clubs, has several shortcomings. The theoretical discussion of matching in this patent separates the dynamic parameters of a golf club into two classes, the dynamic parameter (moment of inertia) and the static parameters (mass and first moment). The differential equations of motion of the swing of a golf club, which are the equations of a well-known double pendulum problem, show that indeed all three of these parameters must be considered as dynamic parameters.
In addition, the matching method disclosed in this patent does not give a unique solution to the matching formulation. To initiate the matching process as described in this patent, a single mass slug is placed at some point in the shaft of the club with the shortest shaft in the set. The determination of the mass of this single mass slug, as well as its location in the shaft of the club, is not disclosed in the patent. Further, the example provided in the patent employs clubs longer and slightly heavier than standard length golf clubs, presumably as a result of the inadequacies of the matching method disclosed.
With a set of golf clubs matched according to the present invention, these difficulties are alleviated. To achieve perfect matching, two quantities of mass are positioned rigidly in the shaft of each golf club according to the present invention. An added mass is positioned rigidly in the shaft at a point one-half the distance between the wristcock axis and the coordinate along the shaft of the center of mass of the club head, and a further mass is positioned in the shaft adjacent the wristcock axis. The positions and quantities of these masses are uniquely determined by the formulation described by the present invention. In addition, clubs of standard lengths may be matched according to the method of this invention. The present invention describes a method of matching golf clubs which overcomes the difficulties of the prior art, and will simplify the manufacture of such clubs in practice.